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Lesson 4, Topic 2
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# Utility Maximization

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Just as the producer aims at maximizing his profit, the consumer aims at maximizing his total satisfaction from what goods and services he consumes. He tries to obtain as many commodities as possible from his limited income. If the consumer consumes one commodity, he will reach his maximum satisfaction when the marginal utility derived from such a commodity is equal to the price of the commodity. For instance, if an individual consumes commodity “X” the marginal utility he derives from this will be given as “MUX” is greater than “PX”, the consumer can increase his satisfaction by buying more units of “X”. But if on the other hand, “MUX” is less than “PX”, the consumer increases his satisfaction by buying less of “X”. This continues until “MUX” = “PX”. The above consideration is the case of a single commodity.

The case of two or more commodities is considered below.

In another case of two or more commodities, if all consumers’ income is spent, the utility derived by spending an additional unit of money must be the same for all commodities; if a consumer derives more utility from a commodity he can increase his satisfaction by spending more on that commodity and less on another. Utility is maximized at the point where;

$$\frac {MUA}{PA} = \frac {MUB}{PB} = \frac {MUC}{PC} = \frac {MUD}{PD}$$

Where MU = Marginal Utility

P = Price of the commodity

In the case of two or more commodities, when a consumer has four goods to consume which are commodity ABCD. If the MU of commodity A is less than the price of it, he will reduce its consumption and consume more of the product that gives higher satisfaction. If the MU of commodity B drops, he will consume more of commodity C. The utility-maximizing will allocate expenditure between commodities in such a way that the satisfaction it gets from all the commodities is equal.

$$\frac {MUX}{PX} = \frac {MUY}{PY} = \frac {MUZ}{PZ}$$

This means that individual will demand each commodity up to the point where the marginal utility per kobo spent on every commodity is the same. Utility is also maximized when the ratio of the utility is equal to the ratio of their price, i.e.

$$\frac {MUX}{PX} = \frac {PX}{PY} = \frac {MUZ}{PZ}= \frac {PY}{PZ}$$

The consumer is at equilibrium or maximize his utility when the above equation are satisfied.

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